The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  1  1  1  1  1  1  1  1  1  1
 0  X  0  0  0  X  X  X a*X  0  X a*X a*X a*X a*X  X a*X a^5*X  0  X  0 a^4*X a^2*X a^4*X a^2*X a^3*X a^2*X a^6*X  X a^3*X a^4*X a*X  0  0 a^5*X a^5*X a^3*X a^2*X a^4*X  X  X  0 a^2*X a^5*X  X  0 a^3*X a^2*X a^2*X  X a^6*X  0
 0  0  X  0  0 a^6*X a^5*X a^4*X a^4*X  X a^3*X a^6*X  0  X a^5*X a^2*X a*X a^6*X a*X  0 a^2*X a*X a^5*X a^2*X a^3*X a^4*X a^3*X a^5*X a^6*X a^5*X a^6*X a^6*X a*X  0 a^4*X  X a^6*X a^2*X  X  X a^5*X  X a^4*X a^5*X a*X  X a^6*X a^6*X a^6*X  X a^2*X  0
 0  0  0  X  0  X a^5*X a*X a^3*X a^2*X a^6*X  0 a^5*X  X a*X a^4*X a^4*X a^4*X a^4*X a*X  X  0  X  X a^5*X a^5*X a*X  0  X a^5*X  0 a^2*X  X a^5*X a^2*X a*X a^2*X a*X a*X a^5*X  X  0 a^6*X a*X  0 a^2*X a^6*X  X a*X  0 a^6*X  0
 0  0  0  0  X a^6*X a^3*X a*X a^5*X a*X a^2*X a^2*X a^3*X  0 a*X  0 a^2*X a^4*X  X a^3*X a^4*X a*X a^3*X  0 a^6*X a^4*X  X  0 a^2*X a^6*X  X a^4*X  X a*X a^3*X a*X a^4*X a^4*X  0  0 a^6*X a^4*X a^4*X a^5*X  X a^6*X a*X a^6*X a^6*X  X a*X a^2*X

generates a code of length 52 over F8[X]/(X^2) who´s minimum homogenous weight is 320.

Homogenous weight enumerator: w(x)=1x^0+245x^320+1484x^328+2352x^336+448x^343+3290x^344+9408x^351+3682x^352+65856x^359+4613x^360+153664x^367+5117x^368+4872x^376+3710x^384+2289x^392+945x^400+140x^408+28x^416

The gray image is a linear code over GF(8) with n=416, k=6 and d=320.
This code was found by Heurico 1.16 in 31.6 seconds.